Derivatives

Step 1:
To find where the function is increasing or decreasing, we first compute the first derivative of the function :
Step 2:
Set to find the critical points: Thus, the critical points are and .
Step 3:
To determine whether the function is increasing or decreasing, we analyze the sign of in each of the intervals defined by the critical points: , , and . For , choose a test point : Therefore, the function is increasing in . For , choose a test point : Therefore, the function is decreasing in . For , choose a test point : Therefore, the function is increasing in .
Step 4:
From the analysis above, we conclude that the function is increasing in and decreasing in .